Я пишу адресу на першій сторінці зошита.

Because адресу is the accusative singular form of адреса.

In this sentence, адресу is the direct object of пишу (I am writing), so it takes the accusative case.

• адреса = nominative singular (an address / the address as the subject or dictionary form)
• адресу = accusative singular (an address as the object)

So:

• Адреса тут. = The address is here.
• Я пишу адресу. = I am writing the address.

На першій сторінці uses the prepositional/locative case because it expresses location: on the first page.

The preposition на often means on or at, and when it describes where something happens, it commonly requires the locative.

Here:

• на = on
• першій = first, in the feminine locative singular
• сторінці = page, in the locative singular

The base form is:

• перша сторінка = first page

But after на for location, it becomes:

• на першій сторінці = on the first page

It is першій because the adjective must agree with the noun сторінці in gender, number, and case.

The noun сторінка is:

• feminine
• singular
• here in the locative case

So the adjective перший (first) changes to match it:

• masculine nominative: перший
• feminine nominative: перша
• feminine locative: першій

That is why we get:

• на першій сторінці

not

• на перша сторінка
• на перший сторінці

Because зошита is the genitive singular form of зошит (notebook/exercise book).

In the phrase сторінці зошита, Ukrainian uses a structure like:

• the page of the notebook

So:

• сторінка = page
• зошит = notebook
• сторінка зошита = page of the notebook

Since зошит depends on сторінка and shows possession/relationship, it goes into the genitive:

• зошита

This is very common in Ukrainian:

• обкладинка книги = the cover of the book
• двері будинку = the door of the house
• сторінка зошита = the page of the notebook

Because Ukrainian does not have articles like a and the.

English says:

• I am writing the address on the first page of the notebook.

Ukrainian simply says:

• Я пишу адресу на першій сторінці зошита.

Whether something is a, an, or the is usually understood from context.

So адресу could mean:

• an address
• the address

depending on the situation.

Yes, it can often be omitted.

Ukrainian verbs usually show the subject clearly, so пишу already means I write / I am writing.

That means both of these are possible:

• Я пишу адресу...
• Пишу адресу...

Both can mean I am writing the address...

The pronoun Я is often included for:

• emphasis
• clarity
• contrast

For example:

• Я пишу адресу, а він малює. = I’m writing the address, and he’s drawing.

It can mean both, depending on context.

Ukrainian present tense often covers both:

• I write
• I am writing

So Я пишу адресу could mean:

• I write the address
• I am writing the address

In many real situations, the natural English translation is I am writing the address.

Also, писати is an imperfective verb, which often focuses on the process or ongoing action rather than completion.

Yes, Ukrainian word order is fairly flexible.

The given order is natural and neutral:

• Я пишу адресу на першій сторінці зошита.

But other orders are possible, depending on emphasis:

• Адресу я пишу на першій сторінці зошита.
  Emphasizes the address.
• На першій сторінці зошита я пишу адресу.
  Emphasizes where I’m writing it.

Even though word order can change, the cases help show the grammatical roles, so the meaning usually stays clear.

Not exactly.

Зошит usually means a notebook, especially a school-style notebook or exercise book.

So:

• зошит = notebook / exercise book
• книга = book

In this sentence, зошита means of the notebook, not of the book.

Here на is used because Ukrainian normally says on a page with на.

So:

• на сторінці = on the page

This matches English quite closely.

Using another preposition here would usually sound unnatural or change the meaning.

For location on a surface or on a page, на is the normal choice.

Because this is a very common Ukrainian noun structure:

• noun + genitive noun

Here:

• сторінці = on the page
• зошита = of the notebook

So together:

• на першій сторінці зошита = on the first page of the notebook

The genitive noun зошита tells you what page it is: the page belonging to or from the notebook.

A rough pronunciation guide is:

Ya py-SHU ad-RE-su na PER-shiy sto-RIN-tsi ZO-shy-ta

A few notes:

• Я sounds like ya
• пишу has stress on the last syllable: пиШУ
• адресу usually has stress on the second syllable: адРЕсу
• першій is roughly PER-shiy
• сторінці is roughly sto-RIN-tsi
• зошита is roughly ZO-shy-ta

If you want to sound more natural, pay attention to stress, since it matters a lot in Ukrainian.